Many in vivo studies examining invasion, intravasation, and distant colonization in mouse models have shown that CXCR4 over-expressing breast cancer cells are greatly sensitive to high levels of CXCL12, creating the potential for enhanced, directed cellular migration in the direction of the gradient [ 62, 63].
When placed in an inhomogeneous field, matter is either attracted or repelled in the direction of the gradient of the field.
This method of optimization involves testing the response surface in the direction of the gradient.
An edge point is defined to be a point whose strength is locally maximum in the direction of the gradient.
Depending on the direction of the gradient, X is then shifted to one of its eight connected points.
The algorithm of gradient descent [12] advances in the opposite direction of the gradient and narrows it to the minimum.
The magnitude and direction of the gradient in an image I x, y) are given by: (14).
They found about 60% of mature sperm swam in the general direction of the gradient, even when the temperature was only half a degree higher.
The dual problem is solved by the gradient descent method, where lagrange multiplier λ is updated along the opposite direction of the gradient ∇D.
The figure on the right shows the window of width W=3 during the current iteration and the general direction of the gradient from the center.
The magnitude of the gradient tells us how quickly the image content is changing, while the direction of the gradient tells us the orientation of these rapid changes.
